CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS

CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS

Bibliographic Details
Main Author: HERAT, ATHULA RAVINDRA
Language:English
Published: University of Cincinnati / OhioLINK 2003
Subjects:
classical solutions
guage fields
field theory
color confinement
QCD
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060257141
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-ucin10602571412021-08-03T06:09:17Z CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS HERAT, ATHULA RAVINDRA classical solutions guage fields field theory color confinement QCD I study the curvature dependence of extended classical solutions of interacting field theories. The main motivation behind my study of classical solutions is confinement. It has become apparent that classical objects (monopoles and vortices) are responsible for color confinement in QCD. Therefore, studying the properties of these objects is extremely important. The main goal of this investigation is to accurately determine the energy of extended classical solutions. In most applications it is assumed that the energy depends simply on the length of the object, irrespective of the shape. I show that the curvature effects are highly non-trivial. I start with the kink solutions of the (2+1) dimensional linear sigma model. In particular, I show that the curvature energy of a kink in two spatial dimensions, as a prototype of extended classical solutions, is always negative. Assuming that the deviations of the kink from the straight line are small, I derive a closed form for the curvature energy. This investigation clearly demonstrates that the energy of the (2+1) dimensional kink has a positive length term and a negative curvature term. Next I look at extended vortex solutions. Vortices are (2+1) dimensional soliton solutions of gauge theories coupled to complex scalar Higgs field. In the trivially extended vortices the core of the vortex forms a straight line. Recent lattice studies show that vortices appear not be straight. Therefore, it is important to study the curvature effects of vortex solutions. However, unlike in the case of the kink, no analytical vortex solutions exist, which makes the study of curved vortices an extremely complex one. This problem can be made less daunting if circular vortices are considered. Therefore, I study the circular vortex of the $U(1)$ gauge theory. I use numerical techniques to obtain the circular vortex configurations that minimize the Hamiltonian. I show that the curvature energy of the circular vortex is negative, which clearly demonstrates that the total energy of the (3+1) dimensional circular vortex is less than the length energy. I.e. the extended abelian vortex prefers the curved state to the straight one. 2003-09-02 English text University of Cincinnati / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060257141 http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060257141 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic classical solutions
guage fields
field theory
color confinement
QCD
spellingShingle classical solutions
guage fields
field theory
color confinement
QCD
HERAT, ATHULA RAVINDRA
CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS
author HERAT, ATHULA RAVINDRA
author_facet HERAT, ATHULA RAVINDRA
author_sort HERAT, ATHULA RAVINDRA
title CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS
title_short CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS
title_full CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS
title_fullStr CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS
title_full_unstemmed CURVATURE DEPENDENCE OF CLASSICAL SOLUTIONS EXTENDED TO HIGHER DIMENSIONS
title_sort curvature dependence of classical solutions extended to higher dimensions
publisher University of Cincinnati / OhioLINK
publishDate 2003
url http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060257141
work_keys_str_mv AT heratathularavindra curvaturedependenceofclassicalsolutionsextendedtohigherdimensions
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